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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0307026 (nlin)
[Submitted on 16 Jul 2003 (v1), last revised 25 Jul 2003 (this version, v2)]

Title:The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I

Authors:P.G.Grinevich (1), P.M.Santini (2) ((1) L.D.Landau Institute for Theoretical Physics,(2) Dipartimento di Fisica, Università di Roma ``La Sapienza'')
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Abstract: This is the first of a series of papers devoted to the study of classical initial-boundary value problems of Dirichlet, Neumann and mixed type for the Nonlinear Schrödinger equation on the segment. Considering proper periodic discontinuous extensions of the profile, generated by suitable point-like sources, we show that the above boundary value problems can be rewritten as nonlinear dynamical systems for suitable sets of algebro-geometric spectral data, generalizing the classical Dubrovin equations.
In this paper we consider, as a first illustration of the above method, the case of the Dirichlet problem on the segment with zero-boundary value at one end, and we show that the corresponding dynamical system for the spectral data can be written as a system of ODEs with algebraic right-hand side.
Comments: 29 pages, LaTeX, 2 Encapsulated Postscript figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Analysis of PDEs (math.AP)
Cite as: arXiv:nlin/0307026 [nlin.SI]
  (or arXiv:nlin/0307026v2 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0307026
Journal reference: American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, 2004, v. 212., pp. 157-178.

Submission history

From: Piotr Grinevich G. [view email]
[v1] Wed, 16 Jul 2003 11:46:12 UTC (33 KB)
[v2] Fri, 25 Jul 2003 12:10:49 UTC (33 KB)
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